MATLAB® and other software

The SPSS (Statistical Product and Service Solutions) and SAS (Statistical Analysis System) are software extensively used for statistical calculations in QA. MATLAB® competes with these as well as other common software programs such as Mathematica, Mathcad, Maple, R (open to free usage), etc., and has gained acceptance in technical computing, which is the area for which it is intended today. Without going into detail, we list here some of the factors that combine to give the advantage to MATLAB®:

■ high universality and suitability for the solution of both simple and complex problems that require original program developments;

■ superb adaptability for various fields of science and engineering with specialized tools, specifically the Statistics Toolbox, which has been adapted for many QA calculations;

■ convenience and diversity of visualization, for general engineering and QA problems;

■ simple and quick access to well-organized and comprehensive documentation.

The purpose and principal audience for this book

The advantages listed above assured the popularity of the software among engineering and scientific audiences in general, and in the field of QA in particularly. They do extensive work with computers and use specialized programs; however, there is a need for a universal tool for solving specific problems in the field of QA. The purpose of this book is to serve as a guide for QA students, teachers, engineers, and scientists. It is assumed that the reader has no prior programming experience and will be using the software for the first time. In order to make clear to the target audience the primary programming steps and the use of commands, these are illustrated by problems from different areas of the quality assurance sciences. Accordingly, the principal audiences for the book are:

■ students, engineers, managers, scientists, and teachers in the field of quality assurance;

■ instructors and their audiences in QA study courses where MATLAB® is used as a supplementary yet necessary tool;

■ personnel in quality-control laboratories, student classes, and non-programmers who use MATLAB®;

■ freshmen and participants in advanced QA courses, seminars or workshops, where MATLAB® is taught;

■ scientists who seek to solve QA-scientific problems and search for similar problems solvable with MATLAB®;

■ self-taught readers, who can quickly master MATLAB® for their needs.

The book will also serve non-QA specialists as a reference for numerical applications that require computer tools for the solution of engineering problems.

About the topics

The topics were chosen based on several years of experience teaching MATLAB® to QA students and specialists. These topics are presented to allow the beginner to progress gradually, with only the previously acquired material prerequisite for each new chapter.

The basic MATLAB® features such as environment, language design, help options, variables, matrix and array manipulations, elementary and special functions, flow chart control, conditional statements, etc., are introduced in the second chapter.

In the third chapter, the visualization tool is introduced with examples of graphic representations of calculations. The material in Chapters 2 and 3 enables the reader to create simple MATLAB® programs.

Chapter 4 introduces commands for probability distributions, random numbers, and special graphs that are available in the Statistics Toolbox and are essential for solving numerous problems in the QA area. The material assumes that the reader has a certain degree of familiarity with probability theory and statistics.

Chapter 5 explains how to write programs in script or function form and save these forms as an m-file. In addition, the supplementary commands for common numerical calculations such as finding solutions for algebraic equations, inter- and extrapolation, differentiation, and integration are described.

The commands for quality-control hypothesis testing (such as Wilcoxon-, t-, z-test, etc.) are briefly described in Chapter 6. Familiarity with statistics is assumed in order to better understand the material presented in this chapter.

In the last chapter (Chapter 7), specific solver commands intended for solving ordinary differential equations (ODE) are briefly presented with examples related to the metrological system, the equilibrium price, and the technological process enhancement. For this chapter, a familiarity with mathematics on a somewhat higher level is assumed.

The Appendix presents the summary tables with a complete set of the MATLAB® characters, operators, commands, and functions explored in this book.

About chapter design and questions for self-checking

Each chapter begins with a short description of the targets. After this, the new tool is described and the main commands for its realization are presented. Each command is explained in one or two of its simplest forms and possible extensions are given; additional information is available in the MATLAB® help or original MATLAB® documentation. Each topic is investigated as completely as possible in one location. Tables with lists of additional available commands, their descriptions and examples, are included in the chapter.

At the end, and occasionally in the middle, of each chapter, application problems from the QA area are introduced together with solutions using the commands accessible to the reader; those given here are the easiest to understand, but are not necessarily the shortest or most original solutions. Readers are encouraged to try their own solutions and compare the results with those in the book.

For a better assimilation of the material, the questions for self-checking are given at the end of each chapter; they contain MATLAB® related questions, and not the QA problems, as this material is intended specifically for the of MATLAB® software. I recommend solving them in order to better understand MATLAB®. The answers to some of these questions are also given at the end of each chapter.

The numerical values and contexts used in the problems are not factual data and serve for learning purposes only.

The MATLAB® versions

Two new versions of MATLAB® appear every year. Each new version is updated and extended. Nevertheless, they are designed to allow work with previously written commands; thus, the basic commands in this book will remain valid in future versions. The version used in the book is R2012b (8.0.0.783). It is assumed that the reader has installed MATLAB® in his/her computer and will be able to perform all basic operations presented in the book.

Order of presentation

The book presents a MATLAB® guide oriented towards those new to computer calculations, and the topics are arranged accordingly, but teachers using the guide may find it necessary to choose their own order of presentations. For example, the commands for probability distributions, random numbers, and special graphs (Chapter 4) can be studied after script- and function-files in Chapter 5 and polynomial and distributional fitting (Subsection 3.3.5) can be presented before hypothesis testing (Chapter 6); script files (Subsection 5.1) can be moved to Chapter 3 directly before the first application examples (Subsection 3.4) to allow students to write script programs already during the first steps; special statistical graphs (Subsections 4.5.1, 4.5.2) can be presented in Subsection 2.3 together with the specialized two- and three-dimensional plots.

I hope the book will be useful for learning MATLAB® software and for applying it to QA problems.

So, here we go.